We acquire information from parents, friends, advisers, salespersons, doctors and so on;
however, conflict of interest affects the way we cope with these information. Consumers tend to be skeptical about salespersons introducing their products because they know salespersons have incentives to lie. This is an example of a strategic sender-receiver game where senders have information advantage and their preferences are not aligned with receivers who make decisions.
The amount of information transmitted is affected by how strong the conflicts of interest are between senders and receivers. Similar examples include analysts vs. investors, doctors vs.
patients, candidates vs. interviewers and so on.
Crawford and Sobel (1982) consider a one-dimensional sender-receiver game of strategic information transmission. A Sender who has full information sends a message to a Receiver, and the Receiver takes an action that decides payoffs of both players. Crawford and Sobel (1982) predict that information transmission decreases as the preference difference between Sender and Receiver increases. They also predict no informative equilibrium exists when conflict of interest is sufficiently large. That is, “babbling equilibrium” is the most informative equilibrium.
Experimental economists have used controlled experiments to test theoretical predictions of Crawford and Sobel (1982). In addition, these experiments are conducted in various numbers of states, messages and actions. Gneezy (2005) reports the senders are more likely to lie when loss to receiver decreases or profit to sender increases in a simple sender-receiver game with 2 states
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x 2 messages x 2 actions. The experiments of Dickhaut et al. (1995) Cai and Wang (2006) and Wang et al. (2010) study the behavior of subjects with different conflict of interest between senders and receivers. Dickhaut et al. (1995) show that as preferences diverge, less information are transmitted in a sender-receiver game with 4 states, 4 actions and messages being single or consecutive sequence of integers from 1 to 4.1 The evidence in Cai and Wang (2006) shows that senders “overcommunicate” and send informative messages to receivers, even though the equilibrium model predicts a “babbling equilibrium”. Cai and Wang (2006) study sender-receiver games with 5 states, 9 actions (5 actions corresponding to each states and 4 intermediate action) and messages being any combination of states.2 Wang et al. (2010) uses eye-tracking to monitor the behavior of senders in sender-receiver games where the numbers of states, messages and actions are all 5. Senders see a state and send one message from {1, 2, 3, 4, 5}, and receivers choose an action from {1, 2, 3, 4, 5}.3
The number of states (and corresponding messages and actions) would influence communication. As the number increases, it is possible for more potential reactions and deception. Hence, the process of information transmission can become more complicated, even though the equilibrium model would predict the same most informative equilibrium.
Sender-receiver games with different parameter space and conditions are extensively studied in the past, but few research compare the results across different state space. We replicate and
1 The messages could be {1}, {2}, {3}, {4}, {1, 2}, {2, 3}, {3, 4}, {1, 2, 3}, {2, 3, 4}, {1, 2, 3, 4}.
2 The states space is {1, 3, 5, 7, 9} and the actions space is {1, 2, 3, 4, 5, 6, 7, 8, 9}. Senders could send messages like {1, 7}, {3, 5} by using or button.
3 The experiments could further extend; for example, allow receivers to costly punish the liars; allow senders to costly keep silence; allow senders to send vague messages; two senders communicate with one receiver and so on [see Sanchez-Pages and Vorsatz (2007, 2009), Serra-Garcia et al. (2011), Vespa and Wilson (2014)].
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modify the experiment design of Wang et al. (2010). Our experiment has two parts, one is the Replicate Treatment with 5 state space as in Wang et al. (2010), and the other is the Simplified Treatment with only 3 state space. The Simplified Treatment uses the similar experimental procedures, but has a smaller state space and fewer biases.4 We focus on the comparison of senders’ behavior in the two Treatments.
We compare the results of the two Treatments. The aggregate and comparative static results show that subject behavior is closer to equilibrium prediction in the Simplified Treatment than the Replicate Treatment. The equilibrium model fails to explain the abundant amount of low-type (L0 and L1) messages, while the level-k model can.
Stahl and Wilson (1994), Nagel (1995), and Camerer et al. (2004) pioneered steps-of-reasoning models of bounded rationality. In the level-k model of Stahl and Wilson (1994) and Nagel (1995), subjects incorrectly believe their opponents have a specific level of bounded rationality, and play best response to this (naïve) belief. In contrast, the cognitive hierarchy model of Camerer et al. (2004) assume subjects have correct but truncated beliefs about others since they cannot image the reasoning of higher types than themselves due to limited cognition.
Crawford (2003) analyses sender-receiver game with level-k model, and sets the L0 sender with truth-telling rather than random-choosing. Costa-Gomes and Crawford (2006) reports that level-k model explains the predictable component of systematic deviations from equilibrium well.
Cai and Wang (2006) uses level-k model to explain their results. Kawagoe (2009) reports that the
4 As the state space decrease, the required “sufficient large” bias which leads to babbling equilibrium will decrease.
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level-k analysis explains their results better than other theories. Our results support the level-k analysis.
Using maximum likelihood estimations, we classified senders into L0 to L2 types and evaluate type classification stability by resampling senders’ choices. 12-14% of senders are classified as L0 type in both Treatments. The proportion of L1 senders decrease from 39% to 25% when the state space decreases from 5 to 3. In contrast, more senders are classified as L2 type in the Simplified Treatment. Resampling of senders’ choices shows that L2 senders are more stable in the Simplified Treatment. These results are consistent with the level-k model (but not cognitive hierarchy) since the more complicated Replicate Treatment should induce senders to think their opponents have lower levels of reasoning.
The remainder of this paper is organized as follows. We formulate some theoretical predictions and propose a set of hypotheses in section 2. Section 3 explains the design of our experiments. Section 4 analyzes our experimental results and section 5 concludes.
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